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DLMF:10.16#Ex8 - MaRDI portal

DLMF:10.16#Ex8 (Q3861)

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DLMF:10.16#Ex8
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    DLMF defining formula
    J - 3 4 ⁡ ( z ) = - 2 - 1 4 ⁢ π - 1 2 ⁢ z - 3 4 ⁢ ( W ′ ⁡ ( 0 , 2 ⁢ z 1 2 ) + W ′ ⁡ ( 0 , - 2 ⁢ z 1 2 ) ) . Bessel-J 3 4 𝑧 superscript 2 1 4 superscript 𝜋 1 2 superscript 𝑧 3 4 diffop parabolic-W 1 0 2 superscript 𝑧 1 2 diffop parabolic-W 1 0 2 superscript 𝑧 1 2 {\displaystyle{\displaystyle J_{-\frac{3}{4}}\left(z\right)=-2^{-\frac{1}{4}}% \pi^{-\frac{1}{2}}z^{-\frac{3}{4}}\left(W'\left(0,2z^{\frac{1}{2}}\right)+W'% \left(0,-2z^{\frac{1}{2}}\right)\right).}}
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